In an electric circuit experiencing drift, a change in an environment condition leads to a normally undesirable change in an operational property of the circuit. Operational properties may include voltage, current, frequency, phase, amplitude, total power, power spectrum, delay, polarization and modulation characteristics. Environment conditions may include external factors, such as fluctuations in ambient temperature, internal temperature, humidity or magnetic flux density, but also internal factors such as variations in signals that are generated expressly for use by the electric circuit, e.g., signals in electric or optical form supplying the circuit with energy, input data or other information. An environment condition may be quantitatively described by a value of an environment parameter.
In a general approach illustrated in FIG. 1A, a circuit 110m, 120m is modelled as a device producing an output signal y(t) in response to an input signal x(t) that the circuit currently receives. If the circuit is assumed to be approximately time-invariant and the input and output signals are modelled as (combinations of) periodic functions of time, the circuit can be characterized quantitatively in terms of its gain G(ω) or phase ϕ(ω) at different values of the frequency ω. The term frequency response is used to refer to a collection of gain or phase values, or both, for frequencies in a relevant frequency range ωa≤ω≤ωb. In the present disclosure, the general notation Q(ω) is meant to cover both gain, phase and any combined representation of both these quantities (complex or otherwise two-dimensional, such as Q(ω)=G(ω) exp(jϕ(ω)) ). The operational properties of a circuit that change because of drift may include gain or phase, or both.
The precise drift behaviour of a circuit may differ quantitatively or qualitatively between different operating frequencies. The frequency dependence of an electric property's drift may be captured by measuring a series of frequency responses under different environment conditions, e.g. a collection of stable values of an observable environment parameter. An equivalent alternative may be to measure the electric property at a collection of stable operating frequencies while the environment conditions are changing in a known fashion.
Other than artificial stabilization of a circuits operating environment, it has been a commonly practised approach for reducing the negative of drift to make direct measurements and then apply a corresponding compensation. The compensation may for instance aim to approach the current output signal (or frequency response) of the circuit to a reference signal (or reference frequency response). The effective drift, i.e. with compensation applied, is thereby reduced.
The applicants earlier disclosure WO14094823A1 is cited as one example, where techniques for compensating a frequency-dependent inphase/quadrature channel mismatch are proposed. Direct measurements may be an attractive option for circuits operating under changing environment conditions, since drift-induced variations are captured as part of the measured signal, and may ultimately be compensated. The approach based on direct measurements may however be computationally costly or otherwise respond relatively slowly.
From the applicant's application WO10069365A1, it is furthermore known that a nonlinearity error in an analog-to-digital converter (ADC) can be estimated—and ultimately compensated—using a plurality of linear filters in accordance with a discrete-time model of the converter that mimics the ADC's behaviour. According to that disclosure, the discrete-time model is tuned to each individual ADC by applying test signals and measuring the corresponding output signal energy. This approach is advantageous by its relatively modest computational expense and low algorithmic delay, but could have accuracy problems unless the ADC is operated under stable environment conditions.